This invention relates to a technology of optical information transmission, and more particularly, to a technology suitable for transmission and reception of an optical signal transmitted via an optical fiber.
For transmission through an extremely high-speed optical fiber, a modulation speed and a transmission distance are limited by chromatic dispersion (CD), polarization mode dispersion (PMD), and bandwidth limit of the optical fiber and components used for the optical fiber.
The chromatic dispersion (CD) is a phenomenon in which light waves different in wavelength are transmitted at different speeds in an optical fiber. An optical spectrum of an optical signal modulated at high speed includes different wavelength components, and the different wavelength components reach a receiving end at different times due to influence of the chromatic dispersion. Thus, it is known that an optical waveform is largely distorted after the transmission. In order to avoid the influence of the chromatic dispersion, a technology of CD compensation (also referred to as dispersion compensation) has been studied. The CD compensation is a technology of, by providing, in an optical transmitter and an optical receiver, an optical device having a chromatic dispersion characteristic opposite to that of an optical fiber used for a transmission line, canceling the chromatic dispersion characteristic of the optical fiber, thereby preventing the optical waveform from being distorted. As an optical device used for the CD compensation, a dispersion compensation fiber, an optical interferometer, an optical circuit, an optical fiber grating, and the like which have chromatic dispersion opposite in sign to that of a transmission line are being studied.
Moreover, a technology of increasing a chromatic dispersion tolerance by improvising a modulation format, and a technology of compensating the chromatic dispersion by signal processing have been proposed. Optical pre-equalization (pre-distortion) transmission according to embodiments of this invention equalizes a field of an optical signal by signal processing carried out in a transmitter. In other words, an optical field waveform is generated in the transmitter by applying an inverse function of chromatic dispersion to a field of an optical signal, and the generated optical field waveform is transmitted via an optical fiber, thereby canceling influence of the chromatic dispersion of the optical fiber. A basic concept of this pre-equalization has existed for several decades, but a digital pre-equalization transmitter which carries out the pre-equalization based on high-speed digital signal processing has recently been proposed. Killey, R, “Dispersion and nonlinearity compensation using electronic predistortion techniques”, Optical Fibre Communications and Electronic Signal Processing, 2005, The IEE Seminar on, Ref. No. 2005-11310 describes a technology of the digital pre-equalization transmitter.
FIG. 2 of above described “Dispersion and nonlinearity compensation using electronic predistortion techniques” illustrates an overall configuration of the pre-equalized optical transmitter, and, in the transmitter, a binary bit sequence to be transmitted (011101 . . . ) is input to a digital signal processor (DSP), and is converted by oversampling into complex field signals (two sets of digital data including the real part and imaginary part) including at least two sampling points per bit. The DSP, by carrying out digital numerical operation, further applies an inverse function of chromatic dispersion of an optical fiber transmission line to the complex field signals constituted by the real part and the imaginary part in advance. The complex field signals to which the inverse function of the chromatic dispersion is applied are transferred to high-speed D/A converters (DACs), which are also working as multiplexing circuits, are converted into analog electric waveforms, and are then input to two electric signal input terminals (I and Q) of an optical field modulator (dual-drive triple Mach-Zehnder modulator in the example illustrated in FIG. 2 of Killey, R, “Dispersion and nonlinearity compensation using electronic predistortion techniques”, Optical Fibre Communications and Electronic Signal Processing, 2005, The IEE Seminar on, Ref. No. 2005-11310), and laser light is converted into a desired optical field ETx (real part I and imaginary part Q), and is output.
The oversampling is carried out by the DSP because the signal is sampled according to the Nyquist's theorem. In other words, the necessary sampling rate is at least twice the highest frequency (corresponding to bit rate Rb) of a signal to be sampled. Thus, generally, for the pre-equalization transmission, extremely high-speed DACs and digital signal processing circuits operating as fast as twice the bit rate (Rb) are necessary.
Moreover, the calculation required for the CD compensation is a linear complex operation of applying an inverse transmission function H(W)=exp(jβLω2/2) of chromatic dispersion of a transmission line to an electrically generated field waveform. In this equation, ω, β, and L respectively denote a difference of angular frequency from the center of an optical signal, a coefficient, and a transmission distance. The digital signal processor (DSP) is realized as a lookup table, a linear FIR filter with complex coefficients, or the like.
This pre-equalization transmission has an advantage that unlimited compensation is theoretically possible for linear degradation. For conventional optical and electrical CD compensation circuits, the quantity of compensation is limited by the size of devices and the loss, but according to the above-mentioned pre-equalization transmission, by increasing the quantity of the digital signal processing, theoretically, unlimited compensation is possible against linear degradation. The chromatic dispersion is an example of linear degradation in transmission employing an optical fiber, and the pre-equalization transmission through a standard single-mode fiber (SMF) is possible for an NRZ signal of 10 Gbit/s over at least 3,000 km.
FIGS. 1A to 1D illustrate a principle and a performance of conventional pre-equalization transmission at 40 Gbit/s of a binary intensity-modulated (IM) signal of 2 samples/bit.
FIG. 1A illustrates an example of an optical field of a 2 sample/bit NRZ signal when pre-equalization quantity is zero, and, as illustrated in FIG. 1A, to a D/A converter, two digital data pieces are input per one bit (section delimited by dotted lines). A solid line represents an electric signal output from the D/A converter, and is an electric waveform smoothly connecting sample points.
An example of FIG. 1B illustrates an optical output waveform obtained by pre-equalization of chromatic dispersion which applies a pre-equalization quantity of −1,000 ps/nm against chromatic dispersion by means of digital signal processing. The optical output waveform illustrated in FIG. 1B is severely distorted, and an eye opening is not observed. However, when the optical output waveform is transmitted through an optical fiber, and chromatic dispersion of 1,000 ps/nm is applied, as illustrated in FIG. 1C, an original eye opening is recovered, and a proper transmission characteristic is obtained.
An example illustrated in FIG. 1D is a result of calculation of evaluating a transmission characteristic of pre-equalization transmission while the chromatic dispersion of a transmission line is compensated 100%. For the pre-equalization, 55-stage and 119-stage FIR filters are used. While, when the 55-stage FIR filter is used, an OSNR penalty (OSNR sensitivity degradation) exceeding 1 dB is generated at a chromatic dispersion quantity of approximately 1,000 ps/nm, when the 119-stage FIR filter is used, transmission is possible without generating an OSNR penalty for a chromatic dispersion quantity exceeding even 1,400 ps/nm. When the number of stages of an FIR filter is limited as in the 55-stage FIR filter, a quantity of chromatic dispersion for which pre-equalization transmission is possible is limited, and the maximum transmission distance is thus determined.
However, the pre-equalization transmission poses the following problems.
A first problem is that high-speed and high-quantity digital signal processing is necessary. For the pre-equalization of chromatic dispersion, high-speed D/A converters operating with processing speed of at least twice the bandwidth of a signal are necessary. Specifically, for signal transmission of a bit rate of 10 Gbit/s, 20 Gsample/second (Sa/sec) is necessary, and, for signal transmission of a bit rate of 40 Gbit/s, 80 GSa/sec is necessary. Further, it is necessary for the pre-equalization processing (FIR filter of several tens of stages) to operate at the same speed.
A second problem is that the quantity of chromatic dispersion which can be pre-equalized decreases rapidly as the bit rate increases. It is known that the distortion in the optical field waveform generated by the chromatic dispersion is proportional to (bit rate)2×(quantity of chromatic dispersion of transmission line). In other words, as the bit rate of signal transmission increases from 10 Gbit/s to 40 Gbit/s, the quantity of chromatic dispersion which can be compensated by a compensation circuit of the same circuit scale (such as a compensation circuit having a lookup table of the same size) decreases to as much as 1/16, resulting in a large decrease in maximum transmission distance.
A third problem is that a chromatic dispersion tolerance does not increase. In the pre-equalization transmission, a transmitter can cancel the chromatic dispersion in advance, but a chromatic dispersion tolerance of an optical signal after transmission does not increase. For example, the dispersion tolerance of an ordinary NRZ signal is 1,200 ps/nm for transmission at a bit rate of 10 Gbit/s, and 80 ps/nm for transmission at a bit rate of 40 Gbit/s. When the pre-equalization of 1,000 ps/nm is carried out, a transmittable range of the signal is 1,000±600 ps/nm for transmission at the bit rate of 10 Gbit/s, and 1,000±40 ps/nm for transmission at the bit rate of 40 Gbit/s. When the chromatic dispersion tolerance is converted into the length of the single-mode fiber (SMF), a length of ±37 km is provided for the transmission at the bit rate of 10 Gbit/s, and a length of ±2 km is provided for the transmission at the bit rate of 40 Gbit/s. It is thus necessary for the pre-equalization to precisely measure the chromatic dispersion quantity of a transmission line in advance or to feed back information on degradation such as chromatic dispersion from a receiver.
Moreover, considering a change in quantity of chromatic dispersion in a transmission line due to a change in temperature, for the transmission at the bit rate of 40 Gbit/s, the chromatic dispersion tolerance becomes insufficient, and it is thus necessary to compensate the deficiency in quantity of chromatic dispersion by a variable CD compensator or the like, resulting in difficulty in cost reduction.
In order to solve the above-mentioned problems, P. Watts, “Performance of Electronic Predistortion Systems with 1 Sample/bit Processing using Optical Duobinary Format”, paper Tu.3.1.6, ECOC, 2007, and M. M. El Said, “An Electrically Pre-Equalized 10-Gb/s Duobinary Transmission System”, Journal of Lightwave Technology, Vol. 23, No. 1, January 2005 describe a 1 sample/bit optical duo-binary pre-equalization which reduces the sampling rate to ½.
FIG. 2 illustrates a configuration of a conventional 1 sample/bit optical duo-binary pre-equalization transmitter 120 described in the above described “Performance of Electronic Predistortion Systems with 1 Sample/bit Processing using Optical Duobinary Format”. In the example illustrated in FIG. 2, when a binary digital signal is input, the input digital signal is input to a duo-binary precoder circuit 103 constituted by a delay-adding circuit, is converted into a duo-binary signal, and is output as a ternary duo-binary signal 113.
The output ternary duo-binary signal 113 is input to a pre-equalization circuit 122 constituted by a lookup table, and is converted into a complex field waveform to which an inverse function of chromatic dispersion is applied according to a bit pattern. For the converted ternary duo-binary signal 113, the real part of the complex field waveform is input to a D/A converter 107-1, and the imaginary part of the complex field waveform is input to a D/A converter 107-2.
The D/A converters 107-1 and 107-2 respectively convert the digital information signal input at 1 sample/bit into an electric waveform of an analog information signal. The converted analog information signals are respectively input to 4-th order Bessel filters 123-1 and 123-2, which are post filters, unnecessary high frequency components are reduced, and the analog information signals are converted into smoothed high-frequency electric waveforms. The converted high-frequency electric waveforms are respectively input to I and Q input terminals of an optical field modulator (IQ modulator) 110, which modulates the real part and imaginary part of an optical signal output from a laser source 101.
Thus, the real part and the imaginary part of the two electric digital signals output from a pre-equalization signal generation circuit 124 are respectively up-converted to the real part and the imaginary part of the output optical field of the pre-equalization transmitter 120. The optical signal output from the transmitter 120 is transmitted through an optical fiber transmission line 111, and is received by an optical receiver 112. When the optical signal is transmitted through the optical fiber transmission line 111, the inverse function of the chromatic dispersion applied by the pre-equalization circuit 122 cancels chromatic dispersion of the optical fiber transmission line 111, and hence an optical waveform without the influence of the chromatic dispersion is theoretically input to the optical receiver 112.
The 1 sample/bit processing is enabled by a fact that the duo-binary signal includes only a half of the frequency bandwidth (half of the bit rate for binary) compared with the intensity modulation. Thus, according to the Nyquist's theorem, even when the sampling rate of the digital signal is reduced by half to 1 sample/bit, the pre-equalization transmission is possible. Moreover, the sampling rate of the D/A converters and the processing speed of the digital signals can also be reduced to a half, thereby reducing the cost, and increasing the system feasibility.